He might be confused at first. Harry isn't always the quickest to understand Hermione's motives right away. So he could just stand there, looking at her with a puzzled expression on his face, not really knowing what he did wrong.
On the other hand, Harry might try to placate Hermione. He values her friendship and doesn't want to have a fight. So he could listen to her concerns and try to explain his reasons for taking Runes. He might promise to be more careful or to follow her advice if she has some to offer, in an attempt to calm her down.
Perhaps Hermione has her own plans regarding Runes. For example, she might have wanted to study Runes with Harry in a particular way or at a certain time. When Harry starts taking Runes on his own or in a different manner, it disrupts her plans, leading to her anger. Also, she could be worried that Harry's approach to Runes might get him into trouble or affect his overall academic progress in a negative way.
One common reason is Hermione's over - protectiveness. Sometimes she tries to control situations too much, which can make Harry feel suffocated and thus angry. For example, in some fanfictions, she might try to stop Harry from taking risks in a dangerous mission, which he sees as her not believing in his abilities.
Harry could initially be in shock. He's always counted on Hermione, so her abandonment would be a huge blow. He might feel a sense of betrayal and confusion.
She could get angry. Hermione, being the strong - willed character she is, might feel betrayed that Harry is leaving. She might yell at him, asking him why he's doing this and how he could leave her after all they've been through together. Her anger is really a mask for her deep sadness and fear of losing him.
She might be initially confused. Hermione is a logical person, and without an obvious reason for Harry's silence, she would be at a loss. She would probably try to think back on their recent interactions to figure out what went wrong.
Perhaps she tries to find them right away. Using her intelligence and resourcefulness, she starts to search for any clues as to where they might have gone. She could ask other friends, like Neville or Luna, if they have seen Harry and Ron. And she might be determined to bring them back, not willing to give up on their friendship easily.
Harry might be really confused at first. He doesn't understand why Hermione is acting so strange. He might try to talk to her about it, but if Hermione is being stubborn, he could get frustrated. He could also be a bit oblivious and just think Hermione is being overprotective as a friend.
He could get angry at Hermione for not believing in him. Maybe he would storm off and then later try to prove his innocence by showing her his study methods or the source of his newfound knowledge. He might also feel betrayed since Hermione is one of his closest friends and her accusation is a serious one.
Harry is usually completely devastated. He might go into a state of shock at first, unable to believe that Hermione is gone. Then he could be filled with anger, either at himself for not being able to protect her or at the situation that led to her death.
He could be initially confused. Harry might not understand why Hermione is suddenly pushing him away. He might try to talk to her to find out the reason, but if Hermione is determined, he could be left feeling hurt and a bit lost.